Video-Doppler-Radar Traffic Surveillance System

ABSTRACT

This invention is related to a Video-Doppler-Radar Traffic Surveillance System comprising of multiple Doppler radars and video cameras, circuitry for processing radar and video signals, and data recording and displaying devices. Although the system is mainly designed for roadside traffic surveillance, it can be used in different applications, such as mounted on a host vehicle or on a UAV. The system will provide continuous surveillance of all incoming and leaving traffic.

TECHNICAL FIELD

The invention relates to a video-Doppler-radar (Vidar) trafficsurveillance system.

BACKGROUND OF THE INVENTION

(1) Doppler Radar Based Traffic Surveillance Systems: A traditionalradar based traffic surveillance system uses a Doppler radar for vehiclespeed monitoring which measures a vehicle speed at line-of-sight (LOS).In FIG. 1, the speed of an approaching (or a leaving) vehicle iscalculated in terms of Doppler frequency f_(D) by

$\begin{matrix}{v_{t} = \frac{f_{D}}{K\; {\cos \left( \varphi_{t} \right)}}} & (1)\end{matrix}$

where K is a Doppler frequency conversion constant. Although a Dopplerradar based system has an advantage of a long detection range, there areseveral difficulties associated with the traditional radar based system,including (1) the Doppler radar beam angle is too large to preciselylocate vehicles within the radar beam; (2) the angle between the vehiclemoving direction and the LOS, φ_(t), is unknown and therefore, needs tobe small enough for a reasonable speed estimation accuracy; (3) sinceall velocity vectors on the equal-Doppler cone in FIG. 1 will generate asame speed, the Doppler radar cannot differentiate the vehicles with asame speed but different directions defined by the same equal-Dopplercone. Therefore, no precise target location information can be derivedin a traditional Doppler radar based traffic surveillance system.

(2) Video Camera Based Traffic Surveillance Systems:

A video camera based traffic surveillance system uses a video camera tocapture a traffic scene and relies on computer vision techniques toindirectly calculate vehicle speeds. Precise vehicle locations can beidentified. However, since no direct speed measurements are availableand the camera has a finite number of pixels, the video camera basedtraffic surveillance system can be used only in a short distanceapplication.

This invention combines the both Doppler radar based system and thevideo based system into a unique traffic surveillance system to preservethe advantages of both systems and overcome the shortcomings of bothsystems.

SUMMARY

A video-Doppler-radar (Vidar) traffic surveillance system to monitortraffic may include a first movable Doppler radar to generate a firstradar beam along the direction of a first motion ray, a second movableDoppler radar to generate a second radar beam along the direction of asecond motion ray, a third fixed Doppler radar to generate a third radarbeam along a direction ray, a video camera to serve as an informationfusion platform by intersecting the first and second radar motion rayswith the camera virtual image plane, a data processing device to processDoppler radar and video information, a tracking device to continuouslypoint the surveillance system to the moving vehicle, and a recordingdevice to continuously record the complete information of the movingvehicle.

The surveillance system may register the first movable radar and thesecond movable radar with the video camera by locating the intersectionsof the first and second movable radar motion rays with the video cameravirtual image plane.

The surveillance system may locate a moving vehicle on the virtual imageplane by intersecting two Doppler circles on the virtual image plane.

The surveillance system may find 3D lines linking Doppler circleintersections to the moving vehicle.

The surveillance system may locate the moving vehicle in 3D space byusing three 3D lines from three frames.

The surveillance system may establish moving vehicle models for formingthe moving vehicle trajectory.

The surveillance system may find the moving vehicle speed by usingDoppler signal from the fixed radar over three frames.

The surveillance system may find the complete vehicle state information,position and velocity, by jointly using three radars and video camera.

The surveillance system may track the moving vehicle by continuouslypointing to the vehicle using the vehicle location on the virtual imageplane.

The surveillance system may record the moving vehicle state informationonto a recording device.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be understood by reference to the followingdescription taken in conjunction with the accompanying drawings, inwhich, like reference numerals identify like elements, and in which:

FIG. 1 illustrates the speed measurement of an approaching vehicle and aleaving vehicle with a Doppler radar;

FIG. 2 illustrates the operational setup of the surveillance system;

FIG. 3 illustrates the lay out of the surveillance system;

FIG. 4 illustrates the functional flow chart of the surveillance system;and

FIG. 5 illustrates registration of the first and second movable Dopplerradars with the video camera.

DETAILED DESCRIPTION

While the term “traffic surveillance” is used herein, it may also referto other traffic applications, such as “traffic monitoring”, etc. Theterm “video” may refer to “any image sequences” which may be generatedby electro-optical or thermal or hyper-spectral devices. The inventiondiscussed here may be applied to the case of multiple video cameras andmore than three radars.

A video-Doppler-radar (Vidar) traffic surveillance system is shown inFIG. 2 where 1—the sensor system which may include a sensorsuite/recording device or apparatus, 2—a target tracking device, 3—thecamera virtual image plane of the video camera 14, 4—a first movingDoppler radar motion ray, 5—a second moving Doppler radar motion ray,6—a radar direction ray connecting the sensor apparatus 1 to a movingvehicle 10, 7—the intersection of the first Doppler radar motion ray 4with the virtual image plane 3, 8—the intersection of the second Dopplerradar motion ray 5 with the virtual image plane 3, 9—the intersection ofa ray connecting the sensor apparatus 1 and the moving vehicle 10, and10 a moving vehicle.

FIG. 3 shows the layout of the sensor apparatus 1 where 11—a firstmoving Doppler radar, 12—a second moving Doppler radar, 13—a fixed orstationary Doppler radar, 14—a fixed or stationary video camera, 15—adata processing device, such as a computer, laptop, personal computer,PDA or other such device, and 16—data recording device, such as a harddrive, a flash drive or other such device.

The functional flow chart of the system is shown in FIG. 4. In thefollowing, we will describe the functional blocks.

1. Register Doppler Radars and Video Camera

The first and second Doppler radars 11,12 in the sensor apparatus 1 maybe extended or retracted or moved side to side as illustrated in steps100, 101, 103 by a motor (not shown) which may be a DC or stepper motoror other movement device and may be moved on sliding tracks (not shown).An optical encoder (not shown) may be mounted on the shaft of the motor,so the sliding speeds of the Doppler radars (ν_(r) ₁ and ν_(r) ₂ in FIG.3) may be predetermined. The sliding track orientation angles (θ_(r) ₁and θ_(r) ₂ in FIG. 3) may be predetermined. Using a calibration method,the intersections (C₁ and C₂ in FIG. 2) of the first and second motionrays 4, 5 with the virtual image planes 3 may be predetermined. Note,this registration method can be applied to a plurality of Doppler radarsand cameras.

It can be seen in FIG. 5, showing the registration of the first andsecond moving Doppler radars 11, 12 with the video camera 14, with thedetermination of C₁ and C₂ that the first and second moving Dopplerradars 11, 12 may be substantially precisely registered with the videocamera 14. The locations of substantially equal-Doppler cones of each ofthe radars 11, 12 may be determined on the camera's virtual image plane3, so that the physical information from the moving vehicle 10 may becalculated from both Doppler and video signals from the first movingradar 11, the second moving radar 12, a stationary Doppler radar 13 andthe video camera 14. The computing device 15 may accept inputs from theabove described elements and may perform the following calculations.

2. Calculate Doppler Frequency of the Moving Vehicle for the k th Frame

Assume the current time is the time of the k th video image frame, i.e.,t=k in steps 105, 106, 107. The Doppler frequencies of the movingvehicle p 10 induced by both moving Doppler radars may be given by

f _(D) _(k) ¹ =K ₁[ν_(t) _(k) cos(φ_(t) _(k) )+ν_(r) _(1k) cos(θ_(r1)_(k) )]  (4)

and

f _(D) _(k) ² =K ₂[ν_(t) _(k) cos(φ_(t) _(k) )+ν_(r) _(2k) cos(θ_(r2)_(k) )].   (5)

where K₁ and K₂ may be Doppler conversion constants for the first andsecond moving Doppler radar (11 and 12 in FIG. 3), and θ_(r1) _(k) ,θ_(r2) _(k) and φ_(t) _(k) are depicted in FIG. 3 with an additionaltime index k. A fixed Doppler radar 13 may be used to sense the movingvehicle motion

f _(D) _(k) ³ =K ₃ν_(t) _(k) cos(φ_(t) _(k) )   (6)

where K₃ is the Doppler conversion constant for the fixed Doppler radar(13 in FIG. 3). Doppler frequencies described by Eqs. (4), (5) and (6)may be obtained at (k+1)th and (k+2)th frames, as in steps 113, 114,115, 120, 121, and 122.

3. Calculate Doppler Difference, Cone Angle and Circle for the k thFrame

In steps 109, 110, since all three radars 11,12,13 may be locatedtogether and assuming that the distance from the sensor suite to themoving vehicle 10 may be much larger than the distance between radars11,12,13, the following Doppler differences may be

$\begin{matrix}{{{\Delta \; f_{D_{k}}^{13}} = {{\frac{f_{D_{k}}^{1}}{K_{1}} - \frac{f_{D_{k}}^{3}}{K_{3}}} = {v_{r_{1\; k}}{\cos \left( \theta_{r_{1\; k}} \right)}}}}{and}} & (7) \\{{\Delta \; f_{D_{k}}^{23}} = {{\frac{f_{D_{k}}^{2}}{K_{2}} - \frac{f_{D_{k}}^{3}}{K_{3}}} = {v_{r_{2\; k}}{\cos \left( \theta_{r_{2\; k}} \right)}}}} & (8)\end{matrix}$

where the impact of the moving vehicle may have been removed. Eqs. (7)and (8) may actually recover the substantially independent motionDoppler signals of the first and second moving Doppler radars 11, 12,except for the conversion constants. The Doppler differences in Eqs. (7)and (8) are the ones for the kth frame.

From Eqs. (7) and (8), since ν_(r) _(1k) and ν_(r) _(2k) are known fromcalibration, Doppler cone angles at t=k may be calculated as

$\begin{matrix}{{{\hat{\theta}}_{r_{1\; k}} = {\cos^{- 1}\left( \frac{\Delta \; f_{D_{k}}^{13}}{v_{r_{1\; k}}} \right)}}{and}} & (9) \\{{\hat{\theta}}_{r_{2\; k}} = {{\cos^{- 1}\left( \frac{\Delta \; f_{D_{k}}^{23}}{v_{r_{2\; k}}} \right)}.}} & (10)\end{matrix}$

Using Doppler cone angles in Eqs. (9) and (10), Doppler circles¹ may beconstructed on the virtual image plane 3, as shown in FIG. 5. Theintersections of the Doppler circles specified by {circumflex over(θ)}_(r) _(1k) and {circumflex over (θ)}_(r) _(2k) may effectivelylocate the vehicle q on the image plane, as shown in FIG. 5. The ghostintersection point, q′, may be easily removed with some physicalconstraints. Doppler differences, cone angles and circles defined byEqs. (7), (8), (9) and (10) may be obtained at (k+1)th and (k+2)thframes, as in steps 116, 117, 123, and 124. ¹ Precisely speaking, thesemay be ellipses. Due to a small angle between radar motion vectors, theellipses may be well approximated as circles.

4. Calculate 3D Lines from Doppler Radar to Vehicle

In step 111, assume the vehicle location is X _(t) _(k)=[x_(t),y_(t),z_(t)]_(k) and moving Doppler motion vectors are ν _(r)_(1k) =[ν_(r) _(1x) ,ν_(r) _(1y) ,ν_(r) _(1z) ]_(k) and ν _(r) _(2k)=[ν_(r) _(2x) ,ν_(r) _(2y) ,ν_(r) _(2z) ]_(k). At t=k, we may have

$\begin{matrix}{{\theta_{r_{1\; k}} = {\cos^{- 1}\frac{{\underset{\_}{X}}_{t_{k}} \cdot {\underset{\_}{v}}_{r_{1\; k}}}{{{\underset{\_}{X}}_{t_{k}}}{{\underset{\_}{v}}_{r_{1\; k}}}}}}{and}} & (9) \\{\theta_{r_{2\; k}} = {\cos^{- 1}{\frac{{\underset{\_}{X}}_{t_{k}} \cdot {\underset{\_}{v}}_{r_{2\; k}}}{{{\underset{\_}{X}}_{t_{k}}}{{\underset{\_}{v}}_{r_{2\; k}}}}.}}} & (10)\end{matrix}$

The Doppler differences may then be calculated as

$\begin{matrix}{\begin{matrix}{{\Delta \; f_{D_{k}}^{13}} = {v_{r_{1\; k}}{\cos \left( \theta_{r_{1\; k}} \right)}}} \\{= \frac{{\underset{\_}{X}}_{t_{k}} \cdot {\underset{\_}{v}}_{r_{1\; k}}}{{\underset{\_}{X}}_{t_{k}}}} \\{= \frac{{v_{r_{{1{xk}}\;}}x_{t_{k}}} + {v_{r_{1{yk}}}y_{t_{k}}} + {v_{r_{1{zk}}}z_{t_{k}}}}{\sqrt{x_{t_{k}}^{2} + y_{t_{k}}^{2} + z_{t_{k}}^{2}}}}\end{matrix}{and}} & \begin{matrix}(11) \\(12) \\(13)\end{matrix} \\\begin{matrix}{{\Delta \; f_{D_{k}}^{23}} = {v_{r_{2\; k}}{\cos \left( \theta_{r_{2\; k}} \right)}}} \\{= {\frac{{v_{r_{{2{xk}}\;}}x_{t_{k}}} + {v_{r_{2{yk}}}y_{t_{k}}} + {v_{r_{2{zk}}}z_{t_{k}}}}{\sqrt{x_{t_{k}}^{2} + y_{t_{k}}^{2} + z_{t_{k}}^{2}}}.}}\end{matrix} & \begin{matrix}(14) \\(15)\end{matrix}\end{matrix}$

Eqs. (13) and (15) may describe two cones with central axes being OC₁and OC₂, where O is the joint of the two cone tips. The ratio of Dopplerdifferences may define a 3D line passing though O, q_(k) and X _(t) _(k)

$\begin{matrix}{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}} = {\frac{{v_{r_{{1{xk}}\;}}x_{t_{k}}} + {v_{r_{1{yk}}}y_{t_{k}}} + {v_{r_{1{zk}}}z_{t_{k}}}}{{v_{r_{{2{xk}}\;}}x_{t_{k}}} + {v_{r_{2{yk}}}y_{t_{k}}} + {v_{r_{2{zk}}}z_{t_{k}}}}.}} & (16)\end{matrix}$

At t=k+1 and t=k+2, the ratios of Doppler differences may become, as insteps 118 and 125,

$\begin{matrix}{{\frac{\Delta \; f_{D_{({k + 1})}}^{13}}{\Delta \; f_{D_{({k + 1})}}^{23}} = \frac{{v_{r_{{1{x{({k + 1})}}}\;}}x_{t_{({k + 1})}}} + {v_{r_{1{y{({k + 1})}}}}y_{t_{({k + 1})}}} + {v_{r_{1{z{({k + 1})}}}}z_{t_{({k + 1})}}}}{{v_{r_{{2{x{({k + 1})}}}\;}}x_{t_{({k + 1})}}} + {v_{r_{2{y{({k + 1})}}}}y_{t_{({k + 1})}}} + {v_{r_{2{z{({k + 1})}}}}z_{t_{({k + 1})}}}}}{and}} & (17) \\{\frac{\Delta \; f_{D_{({k + 2})}}^{13}}{\Delta \; f_{D_{({k + 2})}}^{23}} = \frac{{v_{r_{{1{x{({k + 2})}}}\;}}x_{t_{({k + 2})}}} + {v_{r_{1{y{({k + 2})}}}}y_{t_{({k + 2})}}} + {v_{r_{1{z{({k + 2})}}}}z_{t_{({k + 2})}}}}{{v_{r_{{2{x{({k + 2})}}}\;}}x_{t_{({k + 2})}}} + {v_{r_{2{y{({k + 2})}}}}y_{t_{({k + 2})}}} + {v_{r_{2{z{({k + 2})}}}}z_{t_{({k + 2})}}}}} & (18)\end{matrix}$

which may describe two more 3D lines passing through O, q_(k+1) and X_(t) _(k+1) , and O, q_(k+2) and X _(t) _(k−2) .

5. Target Kinematic and Measurement Modeling

We may need to connect three frames positional information together. Insteps 104 and 108, let's consider a deterministic modeling case first.Assume the vehicle kinematics satisfy a constant velocity (CV) model

or

$\begin{matrix}{\begin{bmatrix}\underset{\_}{X} \\\underset{\_}{\overset{.}{X}}\end{bmatrix}_{k + 1} = {\begin{bmatrix}I & T \\0 & I\end{bmatrix}\begin{bmatrix}\underset{\_}{X} \\\underset{\_}{\overset{.}{X}}\end{bmatrix}}_{k}} & (19) \\{x_{t_{({k + 1})}} = {x_{t_{k}} + {T{\overset{.}{x}}_{t_{k}}}}} & (20) \\{y_{t_{({k + 1})}} = {y_{t_{k}} + {T{\overset{.}{y}}_{t_{k}}}}} & (21) \\{z_{t_{({k + 1})}} = {z_{t_{k}} + {T{\overset{.}{z}}_{t_{k}}}}} & (22) \\{{\overset{.}{x}}_{t_{({k + 1})}} = {\overset{.}{x}}_{t_{k}}} & (23) \\{{\overset{.}{y}}_{t_{({k + 1})}} = {\overset{.}{y}}_{t_{k}}} & (24) \\{{\overset{.}{z}}_{t_{({k + 1})}} = {\overset{.}{z}}_{t_{k}}} & (25) \\{x_{t_{({k + 2})}} = {x_{t_{k}} + {2T{\overset{.}{x}}_{t_{k}}}}} & (26) \\{y_{t_{({k + 2})}} = {y_{t_{k}} + {2T{\overset{.}{y}}_{t_{k}}}}} & (27) \\{z_{t_{({k + 2})}} = {z_{t_{k}} + {2T{\overset{.}{z}}_{t_{k}}}}} & (28) \\{{\overset{.}{x}}_{t_{({k + 2})}} = {\overset{.}{x}}_{t_{k}}} & (29) \\{{\overset{.}{y}}_{t_{({k + 2})}} = {\overset{.}{y}}_{t_{k}}} & (30) \\{{\overset{.}{z}}_{t_{({k + 2})}} = {{\overset{.}{z}}_{t_{k}}.}} & (31)\end{matrix}$

So, if we know {dot over (x)}_(t) _(k) , {dot over (y)}_(t) _(k) andż_(t) _(k) , we may easily connect three frame information. The fixedDoppler radar may provide the vehicle velocity magnitude information,and we may know the LOS direction angles from the moving Doppler radars.Assume that the vectors from O to q_(k), q_(k+1) and q_(k+2) are Oq_(k)=[u_(k),v_(k),f], Oq _(k+1)=[u_(k−1),v_(k+1),f], and Oq_(k+2)=[u_(k−2),v_(k+2),f] where f is the focal length. The fixedDoppler radar measurement at t=k may be

$\begin{matrix}\begin{matrix}{f_{D_{k}}^{3} = {K_{3}v_{t_{k}}\frac{{- {\underset{\_}{Oq}}_{k}} \cdot {\underset{\_}{\overset{.}{X}}}_{k}}{{{\underset{\_}{Oq}}_{k}}{{\underset{\_}{\overset{.}{X}}}_{k}}}}} \\{= {K_{3}\frac{{- {\underset{\_}{Oq}}_{k}} \cdot {\underset{\_}{\overset{.}{X}}}_{k}}{{\underset{\_}{Oq}}_{k}}}} \\{= {K_{3}{\frac{{u_{k}{\overset{.}{x}}_{t_{k}}} + {v_{k}{\overset{.}{y}}_{t_{k}}} + {f{\overset{.}{z}}_{t_{k}}}}{\sqrt{u_{k}^{2} + v_{k}^{2} + f^{2}}}.}}}\end{matrix} & \begin{matrix}(32) \\\; \\\; \\(33) \\\; \\(34) \\(34) \\(34)\end{matrix}\end{matrix}$

At t=k+1 and t=k+2 moments, we may have

$\begin{matrix}{\begin{matrix}{f_{D_{k + 1}}^{3} = {K_{3}\frac{{u_{k + 1}{\overset{.}{x}}_{t_{k + 1}}} + {v_{k + 1}{\overset{.}{y}}_{t_{k + 1}}} + {f{\overset{.}{z}}_{t_{k + 1}}}}{\sqrt{u_{k + 1}^{2} + v_{k + 1}^{2} + f^{2}}}}} \\{= {K_{3}\frac{{u_{k + 1}{\overset{.}{x}}_{t_{k}}} + {v_{k + 1}{\overset{.}{y}}_{t_{k}}} + {f\overset{.}{z_{t_{k}}}}}{\sqrt{u_{k + 1}^{2} + v_{k + 1}^{2} + f^{2}}}}}\end{matrix}{and}} & \begin{matrix}(35) \\\; \\\; \\(36) \\\;\end{matrix} \\\begin{matrix}{f_{D_{k + 2}}^{3} = {K_{3}\frac{{u_{k + 2}{\overset{.}{x}}_{t_{k + 2}}} + {v_{k + 2}{\overset{.}{y}}_{t_{k + 2}}} + {f{\overset{.}{z}}_{t_{k + 2}}}}{\sqrt{u_{k + 2}^{2} + v_{k + 2}^{2} + f^{2}}}}} \\{= {K_{3}\frac{{u_{k + 2}{\overset{.}{x}}_{t_{k}}} + {v_{k + 2}{\overset{.}{y}}_{t_{k}}} + {f{\overset{.}{z}}_{t_{k}}}}{\sqrt{u_{k + 2}^{2} + v_{k + 2}^{2} + f^{2}}}}}\end{matrix} & \begin{matrix}(37) \\\; \\\; \\(38) \\\;\end{matrix}\end{matrix}$

Eqs. (17) and (18) are rewritten as

$\begin{matrix}{{\frac{f_{D_{({k + 1})}}^{13}}{f_{D_{({k + 1})}}^{23}} = \frac{\begin{matrix}{{v_{r_{{1{x{({k + 1})}}}\;}}\left( {x_{t_{k}} + {T{\overset{.}{x}}_{t_{k}}}} \right)} +} \\{{v_{r_{1{y{({k + 1})}}}}\left( {y_{t_{k}} + {T{\overset{.}{y}}_{t_{k}}}} \right)} + {v_{r_{1{z{({k + 1})}}}}\left( {z_{t_{k}} + {T{\overset{.}{z}}_{t_{k}}}} \right)}}\end{matrix}}{\begin{matrix}{{v_{r_{{2{x{({k + 1})}}}\;}}\left( {x_{t_{k}} + {T\underset{.}{o}{tx}_{\;_{t_{k}}}}} \right)} +} \\{{v_{r_{2{y{({k + 1})}}}}\left( {y_{t_{k}} + {T{\overset{.}{y}}_{\;_{t_{k}}}}} \right)} + {v_{r_{2{z{({k + 1})}}}}\left( {z_{t_{k}} + {T{\overset{.}{z}}_{\;_{t_{k}}}}} \right)}}\end{matrix}}}{and}} & (39) \\{\frac{f_{D_{({k + 2})}}^{13}}{f_{D_{({k + 2})}}^{23}} = \frac{\begin{matrix}{{v_{r_{{1{x{({k + 2})}}}\;}}\left( {x_{t_{k}} + {2T{\overset{.}{x}}_{t_{k}}}} \right)} +} \\{{v_{r_{1{y{({k + 2})}}}}\left( {y_{t_{k}} + {2T{\overset{.}{y}}_{t_{k}}}} \right)} + {v_{r_{1{z{({k + 2})}}}}\left( {z_{t_{k}} + {2T{\overset{.}{z}}_{t_{k}}}} \right)}}\end{matrix}}{\begin{matrix}{{v_{r_{{2{x{({k + 2})}}}\;}}\left( {x_{t_{k}} + {2T{\overset{.}{x}}_{\;_{t_{k}}}}} \right)} +} \\{{v_{r_{2{y{({k + 2})}}}}\left( {y_{t_{k}} + {2T{\overset{.}{y}}_{\;_{t_{k}}}}} \right)} + {v_{r_{2{z{({k + 2})}}}}\left( {z_{t_{k}} + {2T{\overset{.}{z}}_{\;_{t_{k}}}}} \right)}}\end{matrix}}} & (40)\end{matrix}$

Solving Eqs. (16), (34), (36), (38), (39) and (40) simultaneously maygive us the positional and velocity information, [x_(t) _(k) ,y_(t) _(k),z_(t) _(k) ,{dot over (x)}_(t) _(k) ,{dot over (y)}_(t) _(k) , ż_(t)_(k) ], completely with the constraint of Eq. (19). Theoretically, wemay calculate the velocity of a target with any heading angle, φ!

We now consider a stochastic modeling case. Assume the vehiclekinematics satisfy a stochastic CV model

$\begin{matrix}{{\left\lbrack \frac{\underset{\_}{X}}{\overset{.}{\underset{\_}{X}}} \right\rbrack_{k + 1} = {{\begin{bmatrix}I & {I\; T} \\0 & I\end{bmatrix}\left\lbrack \frac{\underset{\_}{X}}{\overset{.}{\underset{\_}{X}}} \right\rbrack}_{k} + {\begin{bmatrix}{\frac{1}{2}I\; T^{2}} \\I\end{bmatrix}{\underset{\_}{\rho}}_{k}}}},{{\underset{\_}{\rho}}_{k}\bullet \; {{N\left( {\underset{\_}{0},Q_{k}} \right)}.}}} & (41)\end{matrix}$

From Eq. (16), the positional measurement equation may be

$\begin{matrix}\begin{matrix}{0 = {{\left( {{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {xk}}}} - v_{r_{1\; {xk}}}} \right)x_{t_{k}}} + {\left( {{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {yk}}}} - v_{r_{1\; {yk}}}} \right)y_{t_{k}}} +}} \\{{\left( {{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {zk}}}} - v_{r_{1\; {zk}}}} \right)z_{t_{k}}}} \\{= \left\lbrack {{{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {xk}}}} - v_{r_{1\; {xk}}}},{{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {xk}}}} - v_{r_{1\; {xk}}}},{{\frac{\Delta \; f_{D_{k}}^{13}}{\Delta \; f_{D_{k}}^{23}}v_{r_{2\; {xk}}}} - v_{r_{1\; {xk}}}}} \right\rbrack} \\{{{{\underset{\_}{X}}_{k} + {\underset{\_}{\gamma}}_{x_{k}}},}}\end{matrix} & (42) \\{{\underset{\_}{\gamma}}_{x_{k}}\bullet \; {{N\left( {\underset{\_}{0},R_{x_{k}}} \right)}.}} & (43)\end{matrix}$

The velocity measurement equation may be established from Eq. (34) as

$\begin{matrix}{\begin{matrix}{f_{D_{k}}^{3} = {{{\overset{\_}{u}}_{k}{\overset{.}{x}}_{t_{k}}} + {{\overset{\_}{v}}_{k}{\overset{.}{y}}_{t_{k}}} + {\overset{\_}{f}{\overset{.}{z}}_{t_{k}}} + {\underset{\_}{\gamma}}_{{\overset{.}{x}}_{k}}}} \\{= {{\left\lbrack {{\overset{\_}{u}}_{k},{\overset{\_}{v}}_{k},\overset{\_}{f}} \right\rbrack {\overset{.}{\underset{\_}{X}}}_{k}} + {\underset{\_}{\gamma}}_{{\overset{.}{x}}_{k}}}}\end{matrix}{where}} & \begin{matrix}(44) \\(45)\end{matrix} \\{{{{\overset{\_}{u}}_{k} = {K_{3}\frac{u_{k}}{\sqrt{u_{k}^{2} + v_{k}^{2} + f^{2}}}}},{{\overset{\_}{v}}_{k} = {K_{3}\frac{v_{k}}{\sqrt{u_{k}^{2} + v_{k}^{2} + f^{2}}}\mspace{14mu} {and}}}}{\overset{\_}{f} = {K_{3}{\frac{f}{\sqrt{u_{k}^{2} + v_{k}^{2} + f^{2}}}.}}}} & (46)\end{matrix}$

Eqs. (41), (43) and (45) may form a stochastic system for the vehicleand a Kalman filter may be used to estimate the position and velocity ofthe vehicle. Minimum three scans may be needed to converge.

1. A system of estimating a moving vehicle velocity, comprising: a.generating said moving vehicle location on an image plane, b. generatingsaid moving vehicle location on a 3D line in a 3D reference coordinate,c. generating a speed measurement of said moving vehicle, and d.generating an estimate of said velocity of said vehicle, whereby saidmethod will estimate said vehicle velocity.
 2. A system of estimating amoving vehicle velocity as recited in claim 1, wherein the methodgenerates said vehicle location on said image plane by intersecting twoDoppler circles.
 3. A system of estimating a moving vehicle velocity asrecited in claim 2, wherein the method generates said Doppler circlesfrom Doppler differences.
 4. A system of estimating a moving vehiclevelocity as recited in claim 2, wherein the method generates saidDoppler differences from a movable Doppler radar and a fixed Dopplerradar.
 5. A system of estimating a moving vehicle velocity as recited inclaim 1, wherein the method generates said 3D location of said vehiclein a 3D reference coordinate by linking said vehicle locations on three3D lines.
 6. A system of estimating a moving vehicle velocity as recitedin claim 5, wherein the method generates said 3D line by passing a 3Dline through said Doppler circle intersection and a join of Doppler conetips.
 7. A system of estimating a moving vehicle velocity as recited inclaim 5, wherein the method generates said Doppler cone from a Dopplerangle.
 8. A system of estimating a moving vehicle velocity as recited inclaim 5, wherein the method generates said Doppler angle from Dopplerradar signals.
 9. A system of estimating a moving vehicle velocity asrecited in claim 1, wherein the method generates said speed measurementof said moving vehicle from said fixed Doppler radar.
 10. A system ofestimating a moving vehicle velocity as recited in claim 1, wherein themethod generates said velocity estimate of said moving vehicle by anestimator.
 11. A system of estimating a moving vehicle velocity asrecited in claim 10, wherein said estimator uses at least one vehiclemodel and one measurement model.
 12. A system of estimating a movingvehicle velocity as recited in claim 1, wherein the method uses at leastone movable Doppler radar, at least one fixed Doppler radar, and atleast one video camera.
 13. A system of estimating a moving vehiclevelocity as recited in claim 1, wherein the method uses at least dataprocessing device and at least one data recording device.